Theorem rspcedeqvd

Description: Restricted existential specialization, using implicit substitution. Variant of rspcedvd for equations. (Contributed by AV, 24-Dec-2019)

	Ref	Expression
Hypotheses	rspcedeqvd.1	|- ( ph -> A e. B )
	rspcedeqvd.2	|- ( ( ph /\ x = A ) -> C = D )
Assertion	rspcedeqvd	|- ( ph -> E. x e. B C = D )

Proof

Step	Hyp	Ref	Expression
1		rspcedeqvd.1	|- ( ph -> A e. B )
2		rspcedeqvd.2	|- ( ( ph /\ x = A ) -> C = D )
3	2 1	rspcime	|- ( ph -> E. x e. B C = D )